1. Solve the ODE. (e2y-ycos(xy))dx + (2xe²y - x cos(xy) +2y)dy = 0 2. Solve the IVP. y" + y = g(t) y(0) = 0, y' (0) = 1 - {; t 0 1 } 3. 4. g(t) = Write the general solution of the ODE by finding two power series solutions about the ordinary point x = 0. Write out the first 3 nonzero terms in each series. (x²+1)y" + xy-y=0 Find the charge on the capacitor in an LRC-series circuit if L = 1 henry, R = 4 ohms, C=0.2 farad, and E(t) = 120 volts. The initial charge and the initial current are both zero. 5. Solve the ODE. dy (2x-3)(21) y = dx 6. 2(x-2)(x-1) Find the general solution of the ODE. y"-6y' +9y=x-33x 7. Find the general solution of the ODE on (0,00). 8. x²y" - xy' + y = 2x Solve the IVP. Answer in explicit form. State the interval of validity for your solution. dy dx x(x+1)- +xy = 1 y(e) = 1 Find the general solution of the ODE. 9. y" + 4y = 3 sin(2x)
1. Solve the ODE. (e2y-ycos(xy))dx + (2xe²y - x cos(xy) +2y)dy = 0 2. Solve the IVP. y" + y = g(t) y(0) = 0, y' (0) = 1 - {; t 0 1 } 3. 4. g(t) = Write the general solution of the ODE by finding two power series solutions about the ordinary point x = 0. Write out the first 3 nonzero terms in each series. (x²+1)y" + xy-y=0 Find the charge on the capacitor in an LRC-series circuit if L = 1 henry, R = 4 ohms, C=0.2 farad, and E(t) = 120 volts. The initial charge and the initial current are both zero. 5. Solve the ODE. dy (2x-3)(21) y = dx 6. 2(x-2)(x-1) Find the general solution of the ODE. y"-6y' +9y=x-33x 7. Find the general solution of the ODE on (0,00). 8. x²y" - xy' + y = 2x Solve the IVP. Answer in explicit form. State the interval of validity for your solution. dy dx x(x+1)- +xy = 1 y(e) = 1 Find the general solution of the ODE. 9. y" + 4y = 3 sin(2x)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Solve the ODE.
(e2y-ycos(xy))dx + (2xe²y - x cos(xy) +2y)dy = 0
2.
Solve the IVP.
y" + y = g(t)
y(0) = 0, y' (0) = 1
- {;
t 0<t<1
1
t> 1 }
3.
4.
g(t)
=
Write the general solution of the ODE by finding two power series solutions about
the ordinary point x = 0. Write out the first 3 nonzero terms in each series.
(x²+1)y" + xy-y=0
Find the charge on the capacitor in an LRC-series circuit if L = 1 henry, R = 4
ohms, C=0.2 farad, and E(t) = 120 volts. The initial charge and the initial current
are both zero.
5.
Solve the ODE.
dy
(2x-3)(21)
y
=
dx
6.
2(x-2)(x-1)
Find the general solution of the ODE.
y"-6y' +9y=x-33x
7. Find the general solution of the ODE on (0,00).
8.
x²y" - xy' + y = 2x
Solve the IVP. Answer in explicit form. State the interval of validity for your
solution.
dy
dx
x(x+1)- +xy = 1
y(e) = 1
Find the general solution of the ODE.
9.
y"
+ 4y = 3 sin(2x)
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